Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Data Analysis Exercise**
This exercise involves finding the range and the standard deviation of a given set of data. The data set is as follows:
**Data Set:** 22, 30, 23, 28, 25, 27, 27
**Tasks:**
(a) **Find the Range:**
- The range is calculated by subtracting the smallest value in the data set from the largest value.
- **Solution:**
\[
\text{Range} = 30 - 22 = 8
\]
(b) **Calculate the Standard Deviation:**
- The standard deviation measures the amount of variation or dispersion in a set of values.
- You'll be provided a box to input the standard deviation value, and you're instructed to round the answer to the nearest thousandth.
**Note:** The calculation for standard deviation involves several steps:
1. Find the mean (average) of the data set.
2. Subtract the mean from each data value and square the result.
3. Find the average of these squared differences.
4. Take the square root of this average to obtain the standard deviation.
Remember to round your final answer to the nearest thousandth as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7cef134d-3264-498a-99f5-02f5b4a376f9%2F5212e059-2301-44be-8d46-88227262a57c%2Fbixp7pe_processed.jpeg&w=3840&q=75)
![**Instructions:**
Find (a) the range and (b) the standard deviation for the sample.
**Data Table:**
| Value | Frequency |
|-------|-----------|
| 2 | 4 |
| 3 | 5 |
| 4 | 2 |
| 5 | 1 |
| 6 | 2 |
**Questions:**
(a) The range is [ ].
(Round to one decimal place as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7cef134d-3264-498a-99f5-02f5b4a376f9%2F5212e059-2301-44be-8d46-88227262a57c%2Ft22c4db_processed.jpeg&w=3840&q=75)
NOTE: PLEASE ASK TWO DIFFERENT QUESTIONS INDIVIDUALLY. PLEASE ASK THE SECOND QUESTION AGAIN. WE CAN SOLVE ONE QUESTION AT A TIME.
Step by step
Solved in 5 steps with 5 images
